An environmental model for the interactions of industry with two competing agricultural resources

Abstract In this paper we model the interactive dynamics between normal agriculture, auxiliary agriculture, industry and the ecosphere using a system of ordinary non-linear differential equations. We study the long-term effects of each of these assets on each other. Mathematical analyses of the model equations with regard to invariance of non-negativity, dissipativity of solutions, and local and global analyses of the system’s equilibria are carried out. We establish conditions for the existence of a positive interior equilibrium using the theory of uniform persistence.